Moore-Penrose Pseudoinverse and Applications.
2019 Pure and Applied Mathematics Masters Theses
An underlying theorem due to Gauss and Lengendre asserts that for an over determined system, there are solutions that minimize kAx − bk 2 which is given by the generalized in-verse of the matrix A even when A is singular or rectangular. Our objective is to prove algebraic analogs of this result for arbitrary operators on complex Hilbert spaces and its generalization for the Moore-Penrose Inverse. We employ the generalized inverse matrix of Moore-Penrose to study the existence and uniqueness of the solutions for over- and under-determined linear systems, in harmony with the least squares method.